Haha, yeah they do. I was just wondering if there was a double meaning, like in English. E.g. "I have an apple" could mean I am holding an apple or I am eating an apple. From the subsequent exercises, I assume in Italian it only means the latter.

I assumed here that the sentence "The cook has lunch" meant that the cook had prepared lunch and we were supposed to know it was available. (Like "I have a sandwich. It's right here.") Would "Il cuoco ha il pranzo" not be the correct translation?

To those struggling with this, it is VERY unnatural for English speakers to have to infer words that are not there. Stay with it and practice. If the sentence is truly "The cook eats lunch," then we expect to see "mangia" in there. If it's "The cook has lunch," then we want "ha" in there. It is a very very long process to learn to do without these words. Non-English languages have this all the time.
The very first sentence I saw in Latin 101 was "Villa est villa romana." So I said aloud "House is house Roman." 4 words, and I knew the meanings of them all, so I said them all, in order. The teacher thought I was trying to be funny, but I honestly did not comprehend that it means "THE house is A Roman house." And the adjective coming AFTER the noun? Extremely difficult to grasp in English, but so natural for other languages.